Directed interactions are likely to fundamentally alter the evolution of cooperation, compared to the classic case of bi-directional interactions. Notably, bi-directionality allows for reciprocity. In the bi-directional setting, after an individual imitates her neighbor's behavior, the neighbor will then experience reciprocity – so that two cooperative neighbors help each other, and two defecting neighbors harm each other. This phenomenon of “network reciprocity" [1]} along bi-directional edges is known to facilitate the local spread of cooperation and retard the spread of defection. But reciprocity cannot occur when behavioral imitation occurs along a uni-directional edge: when an individual copies her neighbor's strategy she does not have the opportunity to reciprocate the behavior she has imitated. Since reciprocity is disrupted, directionality may make it difficult, or even impossible, for cooperation to emerge in structured populations.
